Not equal??

ray giraffe

What is your interpretation of this? [latex]A \neq B \neq C[/latex]

I believe this is equivalent to [latex]A \neq B[/latex] AND [latex]B \neq C.[/latex]

However a GMAT book said that it means that A, B and C are all different.

jeepers101

I would agree with the book. To perceive it the way you do the word AND would specifically have to be used.

seandoiler

surely equality (and whence not equality) is transitive, so [latex] A \neq B [/latex] and [latex] B \neq C [/latex] would then mean [latex]A \neq C [/latex]

Pherekydes

seandoiler wrote: »

surely equality (and whence not equality) is transitive, so [latex] A \neq B [/latex] and [latex] B \neq C [/latex] would then mean [latex]A \neq C [/latex]

[latex] A \neq B [/latex] and [latex] B \neq C [/latex] doesn't explicitly rule out [latex]A = C [/latex]

ray giraffe

seandoiler wrote: »

surely equality (and whence not equality) is transitive, so [latex] A \neq B [/latex] and [latex] B \neq C [/latex] would then mean [latex]A \neq C [/latex]

Surely wrong (a whence a Brain Fart)? [latex] 1 \neq 2 [/latex] and [latex] 2 \neq 1 [/latex] would then mean [latex]1 \neq 1 [/latex]

MoogPoo

Yeah OP your definately right. People just see it and it looks like it means that there all different. But sometimes in maths books they'll say something like A != 0 != B, C!= 0, to mean none are equal to 0. cause you can't say A != B != C != 0 cause then A or B could be equal to 0. But I remember having one lecturer who'd always write it like A != B != C != 0. It would drive you insane, I dunno what the confusion is really.

RoundTower

to say A, B and C are all not equal to zero (but could be equal to each other) I would prefer
[latex]\displaystyle{A, B, C \neq 0}[/latex]

to say A, B, C are all different, though, I don't know what to write.
[latex]\displaystyle{A \neq B \neq C}[/latex]
is ambiguous at best, or this thread wouldn't exist.
[latex]\displaystyle{A \neq B \neq C \neq A}[/latex]
is correct and unambiguous, but doesn't scale to four or more variables.
[latex]A, B, C\; \text{ distinct}[/latex]
is maybe the only reasonable solution.

I think in practice if someone writes
[latex]\displaystyle{A \neq B \neq C}[/latex]
they usually mean to imply also A is not equal to C, but you can't be certain.

MathsManiac

Bottom line: you just shouldn't write that!

seandoiler

ray giraffe wrote: »

Surely wrong (a whence a Brain Fart)? [latex] 1 \neq 2 [/latex] and [latex] 2 \neq 1 [/latex] would then mean [latex]1 \neq 1 [/latex]

i've come to realise don't drink and post ;-) what a stupid mistake

red_fox

RoundTower wrote: »

[latex]A, B, C\; \mathrm{ distinct}[/latex]
is maybe the only reasonable solution.

[latex] |\{A, B, C\}|=3[/latex]

Not that I suggest that it's in any way reasonable!

Even worse would be:

[latex] 0 \notin \{A-B,A-C,B-C\}[/latex]
or equivalently
[latex] A-B,A-C,B-C \neq 0[/latex]

(not so bad for three elements, but even a fourth element D would mean six differences.)

Capt'n Midnight

Pherekydes wrote: »

[latex] A \neq B [/latex] and [latex] B \neq C [/latex] doesn't explicitly rule out [latex]A = C [/latex]

If you were using binary then A can only equal C


Does anyone know where one could lookup the standard meanings of mathematical symbols in cases like this ?

Fbjm

A is not equal to B, A is not equal to C, B is not equal to C.

However, A is not equal to B is not the same as saying B is not equal to C.

Let's say A is 1, B is 2 and C is 3.

1 is unequal to 2 isn't the same as 2 is unequal to 3.

Query answered.

RoundTower

that settles it, thanks fbjm.

Fbjm

RoundTower wrote: »

that settles it, thanks fbjm.

No problem